Related papers: APTT: An accuracy-preserved tensor-train method fo…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a…
We consider the development of exponential methods for the robust time discretization of space inhomogeneous Boltzmann equations in stiff regimes. Compared to the space homogeneous case, or more in general to the case of splitting based…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
We develop a novel Monte Carlo strategy for the simulation of the Boltzmann-BGK model with both low-collisional and high-collisional regimes present. The presented solution to maintain accuracy in low-collisional regimes and remove…
An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
Characterizing the ground-state properties of disordered systems, such as spin glasses and combinatorial optimization problems, is fundamental to science and engineering. However, computing exact ground states and counting their…
We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a tensor train (TT) representation with…
Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
We derive rank bounds on the quantized tensor train (QTT) compressed approximation of singularly perturbed reaction diffusion partial differential equations (PDEs) in one dimension. Specifically, we show that, independently of the scale of…
We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into…
A new implicit BGK collision model using a semi-Lagrangian approach is proposed in this paper. Unlike existing models, in which the implicit BGK collision is resolved either by a temporal extrapolation or by a variable transformation, the…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…